Topic 4 - Random Variables and Discrete Probability Distributions

From Uni Study Guides
Jump to: navigation, search

This article is a topic within the subject Business & Economic Statistics.

Contents

Required Reading

Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition, pp. 217-243.

Random Variables & Probability Distributions

[1]

  • X = Random Variable (RV) - A function or rule that assigns a number to an outcome of an experiment
    • Discrete RV – A countable number of values - time, weight or height
    • Continuous RV – Values are uncountable - the rugby, soccer or basketball score
  • Probability Distribution – Assigns a probability to the values of the RV P(X=x)

Discrete Probability Distributions

  • Requirements
    • 0 ≤ P(X=x) ≥ 1 (All probabilities must be between 0 and 1)
    • ∑ P(X=x) = 1 (All probabilities must sum to 1)
  • Population Mean
    • ECON120341.jpg
  • Population Variance
    • ECON120342.jpg

Laws of Expected Value

  • E(c) = c
  • E(X + c) = E(X) + c
  • E(c*X) = c*E(X)
  • E(X + Y) = E(X) + E(Y)

Laws of Expected Variance

  • V(c) = 0
  • V (X + c) = V(X)
  • V(c*X) = c^2 V(x)
  • V(X + Y) = V(X) + V(Y) – 2COV(X,Y)

Bivariate Distributions

[2] Covariance

  • ECON120344.jpg

ECON120343.jpg

This bi-variate distributions shows the join probabilities of X and Y. For example, the probability of X = 2 and Y = 1 is 0.03. The marginal probabilities can be found in the margins. E.g. the P(X=2) = 0.06 + 0.03 + 0.01 = 0.1

End

This is the end of this topic. Click here to go back to the main subject page for Business and Economic Statistics.

References

Textbook refers to Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition,.

  1. Textbook Pg. 217-228
  2. Textbook Pg. 229-242
Personal tools
Namespaces

Variants
Actions
Navigation
Toolbox